where \(A\)  and \(\psi \)  are, respectively, the gauge and scalar
field with charge \(q\) , \(\mathcal {L}(F)\)  denotes the Lagrangian
density of the EN electrodynamics and we take it as [1]}
\(\mathcal {L}(\mathcal {F})= \frac{1}{4b} \left(e^{-b \mathcal {F}}-1\right),\) 
